Optimal. Leaf size=13 \[ \frac{k^{x^2}}{2 \log (k)} \]
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Rubi [A] time = 0.0072021, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {2209} \[ \frac{k^{x^2}}{2 \log (k)} \]
Antiderivative was successfully verified.
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Rule 2209
Rubi steps
\begin{align*} \int k^{x^2} x \, dx &=\frac{k^{x^2}}{2 \log (k)}\\ \end{align*}
Mathematica [A] time = 0.0016624, size = 13, normalized size = 1. \[ \frac{k^{x^2}}{2 \log (k)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 0.9 \begin{align*}{\frac{{k}^{{x}^{2}}}{2\,\ln \left ( k \right ) }} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.941191, size = 15, normalized size = 1.15 \begin{align*} \frac{k^{\left (x^{2}\right )}}{2 \, \log \left (k\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73341, size = 27, normalized size = 2.08 \begin{align*} \frac{k^{\left (x^{2}\right )}}{2 \, \log \left (k\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095293, size = 17, normalized size = 1.31 \begin{align*} \begin{cases} \frac{k^{x^{2}}}{2 \log{\left (k \right )}} & \text{for}\: 2 \log{\left (k \right )} \neq 0 \\\frac{x^{2}}{2} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08108, size = 15, normalized size = 1.15 \begin{align*} \frac{k^{\left (x^{2}\right )}}{2 \, \log \left (k\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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